Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential EquationsThis thesis is devoted to the study of the asymptotic behavior of singularly perturbed partial differential equations and some related free boundary problems arising from these two problems. We study the free boundary problems in the singulary limit and give some characterizations, and use this to study the dynamical behavior of competing species when the competition is strong. These results have many applications in physics and biology.

Devoted to the study of the asymptotic behavior of singularly perturbed differential equations and some related free boundary problems arising from these two problemsThe results of this thesis have many applications in Physics and BiologyNominated by the Graduate University of Chinese Academy of Sciences as an outstanding PhD thesis